Create Multiple Edges at once and align them very precisely with extrude? (Watch Video as Ex.)
It looks to me like he's using Extrude (E) in combination with transform snapping (magnet icon in the header).
You can also toggle transform snapping on the fly by holding &#9096; Ctrl during the modal transform (no need to click the magnet icon constantly):



Where it looks like he extrudes several individual edges, I think he extruded faces but they where hidden due to backface-culling and inverted normals. In the example gif I selected these and flipped their normals with &#9096; Ctrl&#8679; ShiftN to make them visible.

Note that in the video he merged double vertices manually after extruding (W > Remove doubles), but it's possible to have blender do this on the fly by enabling automerge in the header.